The study of billiards is of course a classical mathematical topic, still of wide current interest. Borrowing from Ya. Sinai's ICM survey paper [1]}, “Billiards are dynamical systems which correspond to the uniform motion of a point inside a domain on a Riemmanian manifold with elastic reflections on the boundary. [...] The theory of billiards suggests many beautiful problems.
And, to quote from the preface of S. Tabachnikov's book [2]} (who in turn refers partly to A. Katok): “Billiards is not a
single mathematical theory; [...] it is rather a mathematician's playground where various methods and approaches are
tested and honed.”
